* seriate_* computes a permutation order for rows and/or columns. * permute rearranges a data matrix according to a permutation order. * get_order returns the seriation order for rows and columns.

seriate_average(object, ...)

seriate_rank(object, ...)

permute(object, order, ...)

refine_seriation(object, ...)

# S4 method for CountMatrix
seriate_correspondence(object, margin = c(1, 2), ...)

# S4 method for IncidenceMatrix
seriate_correspondence(object, margin = c(1, 2), ...)

# S4 method for PermutationOrder
get_order(x)

# S4 method for CountMatrix,PermutationOrder
permute(object, order)

# S4 method for IncidenceMatrix,PermutationOrder
permute(object, order)

# S4 method for CA
refine_seriation(
object,
cutoff,
n = 1000,
axes = c(1, 2),
progress = getOption("tabula.progress"),
...
)

# S4 method for CountMatrix
seriate_average(object, margin = c(1, 2), axes = 1, ...)

# S4 method for IncidenceMatrix
seriate_average(object, margin = c(1, 2), axes = 1, ...)

# S4 method for CountMatrix
seriate_rank(object, EPPM = FALSE, margin = c(1, 2), stop = 100)

# S4 method for IncidenceMatrix
seriate_rank(object, margin = c(1, 2), stop = 100)

## Arguments

object, x An $$m \times p$$ data matrix (typically an object of class CountMatrix or IncidenceMatrix. Further arguments to be passed to internal methods. A PermutationOrder object giving the permutation order for rows and columns. A numeric vector giving the subscripts which the rearrangement will be applied over: 1 indicates rows, 2 indicates columns, c(1, 2) indicates rows then columns, c(2, 1) indicates columns then rows. A function that takes a numeric vector as argument and returns a single numeric value (see below). A non-negative integer giving the number of bootstrap replications. An integer vector giving the subscripts of the CA axes to be used. A logical scalar: should a progress bar be displayed? A logical scalar: should the seriation be computed on EPPM instead of raw data? An integer giving the stopping rule (i.e. maximum number of iterations) to avoid infinite loop.

## Value

seriate_* returns a PermutationOrder object.

refine_seriation returns a RefineCA object.

permute returns either a permuted CountMatrix or an IncidenceMatrix (the same as object).

## Note

Refining method can lead to much longer execution times and larger output objects.

## Seriation

The matrix seriation problem in archaeology is based on three conditions and two assumptions, which Dunell (1970) summarizes as follows.

The homogeneity conditions state that all the groups included in a seriation must:

1. Be of comparable duration.

2. Belong to the same cultural tradition.

3. Come from the same local area.

The mathematical assumptions state that the distribution of any historical or temporal class:

1. Is continuous through time.

2. Exhibits the form of a unimodal curve.

Theses assumptions create a distributional model and ordering is accomplished by arranging the matrix so that the class distributions approximate the required pattern. The resulting order is inferred to be chronological.

The following seriation methods are available:

seriate_average

Correspondence analysis-based seriation (average ranking). Correspondence analysis (CA) is an effective method for the seriation of archaeological assemblages. The order of the rows and columns is given by the coordinates along one dimension of the CA space, assumed to account for temporal variation. The direction of temporal change within the correspondence analysis space is arbitrary: additional information is needed to determine the actual order in time.

seriate_rank

Reciprocal ranking seriation. These procedures iteratively rearrange rows and/or columns according to their weighted rank in the data matrix until convergence. Note that this procedure could enter into an infinite loop. If no convergence is reached before the maximum number of iterations, it stops with a warning.

## Correspondence Analysis

refine_seriation allows to identify samples that are subject to sampling error or samples that have underlying structural relationships and might be influencing the ordering along the CA space.

This relies on a partial bootstrap approach to CA-based seriation where each sample is replicated n times. The maximum dimension length of the convex hull around the sample point cloud allows to remove samples for a given cutoff value.

According to Peebles and Schachner (2012), "[this] point removal procedure [results in] a reduced dataset where the position of individuals within the CA are highly stable and which produces an ordering consistent with the assumptions of frequency seriation."

## References

Desachy, B. (2004). Le sériographe EPPM: un outil informatisé de sériation graphique pour tableaux de comptages. Revue archéologique de Picardie, 3(1), 39-56. doi: 10.3406/pica.2004.2396 .

Dunnell, R. C. (1970). Seriation Method and Its Evaluation. American Antiquity, 35(03), 305-319. doi: 10.2307/278341 .

Ihm, P. (2005). A Contribution to the History of Seriation in Archaeology. In C. Weihs & W. Gaul (Eds.), Classification: The Ubiquitous Challenge. Berlin Heidelberg: Springer, p. 307-316. doi: 10.1007/3-540-28084-7_34 .

Peeples, M. A., & Schachner, G. (2012). Refining correspondence analysis-based ceramic seriation of regional data sets. Journal of Archaeological Science, 39(8), 2818-2827. doi: 10.1016/j.jas.2012.04.040 .

refine_seriation, ca

N. Frerebeau

## Examples

## Replicates Desachy 2004 results
## Coerce dataset to abundance matrix
data("compiegne", package = "folio")
compiegne_count <- as_count(compiegne)

## Get seriation order for columns on EPPM using the reciprocal averaging method
## Expected column order: N, A, C, K, P, L, B, E, I, M, D, G, O, J, F, H
(compiegne_indices <- seriate_rank(compiegne_count, EPPM = TRUE, margin = 2))
#> <PermutationOrder: reciprocal ranking>
#> Permutation order for matrix seriation:
#> - Row order: 1 2 3 4 5...
#> - Column order: 14 1 3 11 16 12 2 5 9 13 4 7 15 10 6 8...
## Permute columns
compiegne_new <- permute(compiegne_count, compiegne_indices)

## Plot new matrix
plot_ford(compiegne_new, EPPM = FALSE)

## See the vignette:
if (FALSE) {
utils::vignette("seriation")
}